Square-wave modulation thermoreflectance for metal film thickness measurement

FENG Changwu; ZHANG Bingjiang; YU Wei; JIANG Puqing

您当前的位置：

首页 >

文章列表页 >

Square-wave modulation thermoreflectance for metal film thickness measurement

Optical Sensing and Measurement | 更新时间：2026-07-23

- Square-wave modulation thermoreflectance for metal film thickness measurement
- OPTICAL TECHNIQUE Vol. 52, Issue 4, Pages: 428-433(2026)
- 作者机构：
  
  1.华中科技大学能源与动力工程学院，湖北武汉430074
  2.吉林大学汽车工程学院，吉林长春 130022
  3.瑞士苏黎世仪器中国分公司，上海 200030
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN206
- Received：12 March 2026，
  
  Revised：2026-05-13，
  
  Accepted：04 June 2026，
  
  Online First：23 July 2026，
  
  Published：20 July 2026
- 稿件说明：
移动端阅览
冯昶武,张炳江,余为等.基于方波调制与周期波形分析的热反射金属薄膜测厚方法[J].光学技术,2026,52(04):428-433.

FENG Changwu,ZHANG Bingjiang,YU Wei,et al.Square-wave modulation thermoreflectance for metal film thickness measurement[J].OPTICAL TECHNIQUE,2026,52(04):428-433.
冯昶武,张炳江,余为等.基于方波调制与周期波形分析的热反射金属薄膜测厚方法[J].光学技术,2026,52(04):428-433. DOI：

FENG Changwu,ZHANG Bingjiang,YU Wei,et al.Square-wave modulation thermoreflectance for metal film thickness measurement[J].OPTICAL TECHNIQUE,2026,52(04):428-433. DOI：

摘要

针对常规热反射技术（TDTR/FDTR）在测量光学不透明金属薄膜厚度时对高热反射系数材料（如铝、金）存在依赖、难以拓展至银、铜等低热反射系数材料的瓶颈，提出一种基于方波调制加热与周期性波形分析仪（PWA）幅值探测的非接触测量方法。通过谐波能量充分利用与深度相位平均，显著提升了低热反射系数材料的信噪比。针对熔融石英衬底上~200nm银膜/铜膜，采用双频测量实现参数解耦，测量厚度与SEM标定值偏差

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=113596846&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=113596829&type=

8.38199997

2.96333337

。方法突破了常规热反射对金属种类的限制，填补了椭偏仪等光学干涉方法在不透明金属膜厚度测量上的盲区，为超薄金属膜在线监测提供了有效手段。

Abstract

Conventional thermoreflectance techniques （TDTR/FDTR） exhibit a selective dependence on high-thermoreflectance metals （such as aluminum and gold） when measuring the thickness of optically opaque metal films

making it difficult to extend to low-thermoreflectance materials like silver and copper. To address this bottleneck

a non-contact measurement method is presented employing square-wave modulated heating and periodic waveform analyzer （PWA） amplitude detection. By exploiting the rich harmonic content of square waves and deep phase averaging

the signal-to-noise ratio is significantly enhanced for low-thermoreflectance materials. A dual-frequency measurement strategy enables effective parameter decoupling. Validation on ~200 nm silver and copper films deposited on fused silica substrates yields measured thickness with deviations within 5% from SEM reference values. This approach breaks through the material-selective restriction of conventional thermoreflectance methods

bridging the capability gap for optically opaque metal films where ellipsometry is ineffective

and provides an effective technique for nondestructive online thickness monitoring.

关键词

Keywords

references

Yun J . Ultrathin metal films for transparent electrodes of flexible optoelectronic devices [J ] . Advanced Functional Materials , 2017 , 27 （ 18 ）: 1606641 .

Kang G , Kwon G , Jeon J , et al . Electromagnetic interference shielding using metal and MXene thin films [J ] . Nature , 2025 , 647 （ 8089 ）: 356 — 363 .

Chen Z , Yang S , Huang J , et al . Flexible, transparent and conductive metal mesh films with ultra-high FoM for stretchable heating and electromagnetic interference shielding [J ] . Nano-Micro Letters , 2024 , 16 （ 1 ）: 92 .

Ma D , Ji M , Yi H , et al . Pushing the thinness limit of silver films for flexible optoelectronic devices via ion-beam thinning-back process [J ] . Nature Communications , 2024 , 15 （ 1 ）: 2248 .

Wen S , Xue X , Wang S , et al . Metasurface array for single-shot spectroscopic ellipsometry [J ] . Light: Science & Applications , 2024 , 13 （ 1 ）: 88 .

任飞旭 , 曲国峰 , 张鑫 , 等 . 基于扫描电镜和能谱仪的薄膜表面形貌和厚度同时测量研究 [J ] . 分析科学学报 , 2023 , （ 3 ）: 355 — 360 .

Ren Feixu , Qu Guofeng , Zhang Xin , et al . Simultaneous measurement of thin film surface morphology and thickness based on scanning electron microscope and energy dispersive spectrometer [J ] . Journal of Analytical Science , 2023 （ 3 ）: 355 — 360 .

Beltrán-Pitarch B , Guralnik B , Borup K A , et al . Temperature coefficient of resistance and thermal boundary conductance determination of ruthenium thin films by micro four-point probe [J ] . Measurement Science and Technology , 2024 , 35 （ 6 ）: 066012 .

Sitko R . Quantitative X-ray fluorescence analysis of samples of less than ‘infinite thickness’: Difficulties and possibilities [J ] . Spectrochimica Acta Part B: Atomic Spectroscopy , 2009 , 64 （ 11-12 ）: 1161 — 1172 .

Cahill D G . Analysis of heat flow in layered structures for time-domain thermoreflectance [J ] . Review of Scientific Instruments , 2004 , 75 （ 12 ）: 5119 — 5122 .

Schmidt A J , Cheaito R , Chiesa M . Characterization of thin metal films via frequency-domain thermoreflectance [J ] . Journal of Applied Physics , 2010 , 107 （ 2 ）: 024908 .

Jiang P , Huang B , Koh Y K . Accurate measurements of cross-plane thermal conductivity of thin films by dual-frequency time-domain thermoreflectance （TDTR） [J ] . Review of Scientific Instruments , 2016 , 87 （ 7 ）: 075101 .

Regner K T , Majumdar S , Malen J A . Instrumentation of broadband frequency domain thermoreflectance for measuring thermal conductivity accumulation functions [J ] . Review of Scientific Instruments , 2013 , 84 （ 6 ）: 064901 .

Wilson R B , Apgar B A , Martin L W , et al . Thermoreflectance of metal transducers for optical pump-probe studies of thermal properties [J ] . Optics Express , 2012 , 20 （ 27 ）: 28829 .

A quantitative SNR comparison : Lock-in amplifier vs . Boxcar averager | zurich instruments [EB/OL ] . [ 2026-05-12 ] . https://www.zhinst.cn/china/en/blogs/quantitative-snr-comparison-lock-in-amplifier-vs-boxcar-averager/ https://www.zhinst.cn/china/en/blogs/quantitative-snr-comparison-lock-in-amplifier-vs-boxcar-averager/ .

Zurich Instruments . Principles of boxcar averaging （White Paper） [R ] . Zurich Instruments , 2021 .

陈韬 , 江普庆 . 揭示热反射实验中热物性参数的本征关系 [J ] . 物理学报 , 2024 , 73 （ 23 ）: 230202 .

Chen Tao , Jiang Puqing . Unraveling intrinsic relationship of thermal properties in thermoreflectance experiments [J ] . Acta Physica Sinica , 2024 , 73 （ 23 ）: 230202

Chen T , Jiang P . Decoupling thermal properties in multilayered systems for advanced thermoreflectance experiments [J ] . Physical Review Applied , 2025 , 23 （ 4 ）: 044004 .

Touloukian Y , Buyco E . Thermophysical properties of matter-the tprc data series . volume 4 . specific heat-metallic elements and alloys[M ] . DTIC Document , New York, Washington ; 1971.

Touloukian Y , Powell R , Ho C , et al . Thermophysical properties of matter-the TPRC data series . volume 2 . thermal conductivity nonmetallic solids[M ] . IFI/Plenum , New York, Washington , 1970.

Touloukian Y , Buyco E . Thermophysical properties of matter-the tprc data series . volume 5 . specific heat-nonmetallic solids[M ] . New York, Washington : DTIC Document , 1971.

Jiang P , Wang D , Xiang Z , et al . A new spatial-domain thermoreflectance method to measure a broad range of anisotropic in-plane thermal conductivity [J ] . International Journal of Heat and Mass Transfer , 2022 , 191 : 122849 .

Ashcroft N , Mermin N . Solid state physics [M ] . Saunders College , 1976 .

Jain A , McGaughey A J . Thermal transport by phonons and electrons in aluminum, silver, and gold from first principles [J ] . Physical Review B , 2016 , 93 （ 8 ）: 081206 .

Chen T , Song S , Shen Y , et al . Simultaneous measurement of thermal conductivity and heat capacity across diverse materials using the square-pulsed source （SPS） technique [J ] . International Communications in Heat and Mass Transfer , 2024 , 158 : 107849 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Lens centering and sensor positioning for the wide-field high-definition camera

Study on a method for evaluating geometric tolerances based on monocular rotational vision

Hyperspectral gunshot residue detection based on depth-separable convolution and channel attention mechanism

Monocular-vision measurement of street-tree parameters by integrating depth-space correction and geometric anchors

SiNx/SiOx multilayer stacks as flexible OLED substrates for automotive tail lights

Related Author

No data

Related Institution

No data

⁰